Mathematical Analysis of Hepatitis B Virus Transmission Dynamics in the Absence of Therapy with Atangana-Baleanu Fractional -Order SPQWXY Model
Otugene Victor Bamigwojo *
School of Preliminary and Remedial Studies (SPRS), Federal University Lokoja (FUL), Nigeria.
Mbah Christopher Godwin Ezike
Faculty of Physical Sciences, University of Nigeria Nsukka (UNN), Nigeria.
Paul Owhenagbo
Department of Bioinformatics, University of Arkansas Little Rock, United State of American.
Idoko Peter Idoko(OP)
Faculty of Physical Sciences, University of Nigeria Nsukka (UNN), Nigeria.
Jeremiah Damilila Adedoyin
Department of Mathematics, University of Nevada, Reno, USA.
Lawrence Anebi Enyejo
Department of Mathematics, Chukwuemaka Odumegu University, Nigeria.
Agina Precious Chikaedum
Department of Mathematics, Chukwuemaka Odumegwu Ojukwu University Awka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper presents an innovative fractional order network model aimed at elucidating the transmission dynamics of Hepatitis B Virus (HBV). Incorporating fractional calculus enables the model to capture the intricate, memory-dependent mechanisms inherent in HBV spread, thereby overcoming the constraints of conventional integer order models. The primary objective of the study is to develop a more precise depiction of HBV transmission, encompassing both vertical and horizontal routes in the absence of vaccination strategies. Furthermore, the paper assesses the existence and uniqueness of solutions utilizing the Banach fixed point theory with the Picard-Lindelf approach. Numerical simulations conducted across various fractional orders reveal that as the fractional order decreases from 1, the rate of endemic spread decelerates.
Keywords: SPQWXY HBV-virus model, atangana-baleanue fractional derivative, picard-linderlof approach, fixed point theory